1. Field of the Invention
The present invention is directed to probe-based instruments and, more particularly, relates to a method and apparatus for facilitating high speed dynamic and quasi-static measurements using such an instrument. In a particularly preferred embodiment, the invention relates to the control of such an instrument to reduce or minimize lateral forces on the probe in order, e.g., to facilitate quantitative indentation measurements on the nanoscale. The invention additionally relates to the taking of indentation measurements using a probe based instrument.
2. Description of Related Art
Several probe-based instruments monitor the interaction between a cantilever-based probe and a sample to obtain information concerning one or more characteristics of the sample. For example, scanning probe microscopes (SPMs) typically characterize the surface of a sample down to atomic dimensions by monitoring the interaction between the sample and a tip on the cantilever probe. By providing relative scanning movement between the tip and the sample, surface characteristic data can be acquired over a particular region of the sample, and a corresponding map of the sample can be generated.
The atomic force microscope (AFM) is a very popular type of SPM. The probe of the typical AFM includes a very small cantilever which is fixed to a support at its base and which has a sharp probe tip attached to the opposite, free end. The probe tip is brought very near to or into contact with a surface of a sample to be examined, and the deflection of the cantilever in response to the probe tip's interaction with the sample is measured with an extremely sensitive deflection detector, often an optical lever system such as described in Hansma et al. U.S. Pat. No. RE 34,489, or some other deflection detector such as strain gauges, capacitance sensors, etc. The probe is scanned over a surface using a high-resolution three axis scanner acting on the sample support and/or the probe. The instrument is thus capable of creating relative motion between the probe and the sample while measuring the topography, elasticity, or some other surface property of the sample as described, e.g., in Hansma et al. U.S. Pat. No. RE 34,489; Elings et al. U.S. Pat. No. 5,226,801; and Elings et al. U.S. Pat. No. 5,412,980.
AFMs may be designed to operate in a variety of modes, including contact mode and oscillating mode. In contact mode operation, the microscope typically scans the tip across the surface of the sample while keeping the force of the tip on the surface of the sample generally constant. This effect is accomplished by moving either the sample or the probe assembly vertically to the surface of the sample in response to sensed deflection of the cantilever as the probe is scanned horizontally across the surface. In this way, the data associated with this vertical motion can be stored and then used to construct an image of the sample surface corresponding to the sample characteristic being measured, e.g., surface topography. Alternatively, some AFMs can at least selectively operate in an oscillation mode of operation such as TappingMode™ (TappingMode is a trademark of Veeco Instruments, Inc.) operation. In TappingMode™ operation the tip is oscillated at or near a resonant frequency of the cantilever of the probe. The amplitude or phase of this oscillation is kept constant during scanning using feedback signals, which are generated in response to tip-sample interaction. As in contact mode, these feedback signals are then collected, stored, and used as data to characterize the sample.
Regardless of their mode of operation, AFMs can obtain resolution down to the atomic level on a wide variety of insulating or conductive surfaces in air, liquid or vacuum by using piezoelectric scanners, optical lever deflection detectors, and very small cantilevers fabricated using photolithographic techniques. Because of their resolution and versatility, AFMs are important measurement devices in many diverse fields ranging from semiconductor manufacturing to biological research.
One potentially problematic characteristic of AFMs and other probe-based instruments lies in the inability to obtain some types of nanomechanical quantitative measurements at sufficiently high speeds and/or with sufficient accuracy to meet the ever increasing demands of industry and science.
For example, AFM's have traditionally been incapable of obtaining precise quantitative measurement of some mechanical properties. This inability is increasingly problematic because the demand for such measurements is rapidly increasing. For instance, polymers are being used with increasing frequency in the semiconductor industries as “low-k dielectrics” to fill the gaps or trenches in capacitors used in memory devices. The low-k dielectrics may have a width of 100 nanometers or less. It is often desirable to determine the mechanical properties of these materials.
As another example, nanophase materials such as “block copolymers” (formed from blends of two highly dissimilar polymers) are being used in a variety of applications. It is often desirable to measure the composition and structure of these materials on the nanometer scale. Both types of measurement require the acquisition of data obtained from an indentation measurement performed by monitoring the response of a probe as the probe indents the sample surface. The resultant data can be used to determine elasticity modulus, plastic deformation, and other mechanical characteristics. Prior AFM's can obtain qualitative indentation measurements using a so-called “compositional imaging” technique, but could not obtain quantified measurements.
Several hurdles prevent the transformation of traditional qualitative instruments into high speed and high bandwidth quantitative tools for these nanomechanical quantitative measurements. It has been discovered that one of the key barriers arises from lateral forces that are applied to the probe as result of cantilever bending. To apply a force to the sample for the purposes of, e.g., obtaining an indentation measurement, the fixed end of the cantilever is moved vertically through a distance Δz with the tip in contact with the sample. The resultant cantilever bending generates a force k·Δz, where k is the spring constant of the cantilever. This force is not, however, applied normal to the cantilever. A component of the force instead is imposed laterally or along the length of the cantilever. This component was historically deemed to be non-problematic because the lateral component of the applied force vector is typically assumed to be much smaller than the normal component. However, it has been discovered that the lateral force can in fact be an order of magnitude higher than the normal force.
The reasons for this somewhat counterintuitive characteristic of AFM operation can be appreciated from FIG. 1, which schematically shows an AFM probe P interacting with a sample S during an indenting operation. The probe P includes a cantilever C having a tip T. The cantilever C is fixed on or formed integrally with a base B. The probe P is typically inclined at an angle α of about 10° to 15° relative to the surface of the sample S in order to assure adequate clearance between the probe holder and the sample and in order to facilitate data acquisition by a probe detector assembly. As the probe-sample spacing in the z direction is decreased (by movement of the probe P toward the sample and/or by movement of the sample S toward the probe P in the Z direction) to increase the indentation force, the lateral distance available to the cantilever C in the plane L decreases. This decrease creates a compressive strain along the length of the cantilever C. Since the cantilever C has a much higher stiffness along its length in the plane L than perpendicular to its length in the plane N, the majority of the applied force is actually directed in the lateral direction in the plane L.
It has also been discovered that mounting the probe P horizontally to reduce the angle α to zero does not eliminate the lateral forces on the cantilever C because of the intrinsic asymmetry of the cantilever probe configuration. The imposition of the unintended lateral force on the cantilever C causes a host of problems, including lateral motion of the tip T during indenting, convolution of frictional effects with elastic properties, and non-axially symmetric application of the indenting force.
Some current AFM indentation tools attempt to reduce the lateral forces on a probe by moving the probe laterally away from the indentation point as the probe-sample spacing decreases. The control of this movement is open-loop based upon historical data. It assumes the absence of hysteresis and a constant cantilever angle. Both assumptions usually prove inaccurate in practice, resulting in less than optimal lateral force counteraction.
Axially symmetric indenters have been developed. However, these instruments have low mechanical bandwidth (on the order of 300 Hz) and relatively poor sensitivity because these are subject to high levels of noise. For instance, MTS and Hysitron produce nano-indentation devices in which an indenter tip such as a Berkovich tip is driven into a sample using a multi-plate capacitor transducer system. The device has drive and pickup plates mounted on a suspension system. It provides relative movement between the plates when the forces applied to the pickup plates drive the probe into contact with the sample. The change in space between the plates provides an accurate indication of the probes vertical movement. The input actuation forces and vertical position readout are therefore all-decoupled, resulting in a generally purely symmetrical indentation process. In practice, the sensor element is mounted on a scanning tunnel microscope, and a sample is mounted on the sensor. The force sensor then can be used for both measuring the applied force during micro indentation or micro hardness testing and for imaging before and after the testing to achieve an applied AFM-type image of the surface before and after the indentation process. Systems of this type are described, e.g., in U.S. Pat. Nos. 5,576,483 to Bonin and 6,026,677 to Bonin, both assigned to Hysitron Incorporated.
While the indenter described above provides axially symmetric indentation, it has a very low bandwidth because of the relatively large mass of the capacitive plates. The instrument also cannot obtain an accurate image of indentations, particularly in relatively elastic samples, because of sample rebound between the indentation and image acquisition passes and because of the large tip radius inherent in the indenter tip. It also has relatively poor force sensitivity, on the order of 15 nano-Newtons, as opposed to a few pico-Newtons for a true AFM having a much smaller tip.
Other obstacles have also heretofore prevented AFM-based quantitative indentation measurements.
For instance, prior AFM-based indenters, like other indenters, indented the sample and acquired indentation data in two separate steps. That is, the sample is first indented using a probe to create an indent. Then, after the probe is removed from the indent, a raster scan or similar scanning technique is used to image the indent. However, the acquired image does not accurately reflect the indent for at least two reasons. First, the tip cannot accurately reflect deformation geometry. Second, an elastic material will at least partially recover or “rebound” between the indentation and imaging passes, resulting in partial disappearance of the indentation. In the worst case scenario of a near perfectly elastic sample surface, the indentation will nearly completely disappear between the indentation and imaging passes.
For instance, the displacement of a material in response to a given load provides useful information regarding property characteristics, including elastic modulus Esample and the plastic deformation. Loads are typically imposed by indenting a sample surface with a probe and measuring properties of the resulting indentation. The sample is indented through an indentation cycle having a “loading phase” in which the tip is driven into and indents the sample surface and a subsequent “unloading phase” in which the tip is withdrawn from the sample surface.
The load-displacement relationship resulting from an indentation cycle is expressed in the form of Hook's law for indentation induced deformations. Hook's law, which expresses the relationship between force and deformation, is expressed as follows:L=a(hmax−hf)m  (1)
where:                L is the load applied to the cantilever probe,        hmax, or penetration depth, represents maximum tip penetration into the sample during the indentation cycle; and        hf, or plastic indentation depth, is the plastically deformed part of the penetration depth hmax which does not recover after load withdrawal.        
During a typical indentation cycle, the loading probe will indent the sample to hmax at the end of the loading phase when the applied load is the highest. Then, during the unloading phase, the unloading probe will separate from the bottom of the indentation at a release point Pr above the point Pmax located at the lower limit of hmax. The derivative of equation (1) is called contact stiffness, S. S at any given depth h during deformation can be expressed as:
                    S        =                              ⅆ            L                                ⅆ            h                                              (        2        )            
The static contact stiffness for an entire indentation cycle can be expressed as:
                    S        =                              Δ            ⁢                                                  ⁢            L                                Δ            ⁢                                                  ⁢            h                                              (        3        )            
If lateral forces on the tip are counterbalanced, ΔL can be easily determined simply by detecting the vertical load, Lmax, at the end of the loading phase of the indentation cycle. Δh can be determined by subtracting the maximum penetration point Pmax from the initial contact point, Pic, where the probe first engages the sample surface. Pmax can be measured directly using conventional monitoring techniques. Pic measurements are more difficult, and are part of a preferred embodiment of the invention.
S is dependent upon material properties as follows:
                    S        =                              2                          π                                ⁢                      E            r                    ⁢                                    A              con                                                          (        4        )            
where                Er is the reduced modulus of the sample/tip interaction; and        Acon is the contact area during deformation, which is a function of indentation depth h;        
The relationship between the elastic modulus of the Esample and Er can be expressed as follows:
                              1                      E            r                          =                                            (                              1                -                                  v                  sample                  2                                            )                                      E              sample                                +                                    (                              1                -                                  v                  tip                  2                                            )                                      E              tip                                                          (        5        )            
where:                Etip is the elastic modulus for the tip, which is known for a tip of a known material, and        Vsample and Vtip are the Poisson ratio for the sample and the tip, respectively.        
Poisson ratios vary only minutely from material to material, so Vsample can be assumed to be close to Vtip, which is a known constant C for a known tip material. Hence, equation 5 can, as a practical matter, be reduced to:
                              1                      E            r                          =                                            (                              1                -                                  c                  2                                            )                                      E              sample                                +                                    (                              1                -                                  c                  2                                            )                                      E              tip                                                          (        6        )            Referring again to Equation (4), Er can be determined from a measured contact area Acon using the equation:
                              E          r                =                                            π                                      2              ⁢                                                A                  con                                                              ⁢          s                                    (        7        )            Hence combining equations (6) and (7), the sample elastic modulus Esample can be determined as follows:
                              E          sample                =                              (                          1              -                              c                2                                      )                    /                      (                                          (                                  2                  ⁢                                                                                    A                        com                                                              /                                                                  π                        )                                                                                            )                            -                                                (                                      1                    -                                          c                      2                                                        )                                                  E                  tip                                                      )                                              (        8        )            
Practically speaking, the greatest challenge for quantitative mechanical measurements is to measure the contact area, Acon, which is a function of the actual contact depth, hcact, and the tip shape. The actual contact depth usually is not the same as the penetration depth, hmax, because a sample having any elasticity will deform away from the tip at the upper portion of the indentation, leaving a space, hs, between the upper limit of the hcact and the initial contact point Pic, as can be appreciated from FIG. 13A. The possible variations in this discrepancy can be appreciated from a comparison of FIG. 14A and FIG. 14B, which illustrate the indentation of the same tip T into the highly plastic sample S1 and a highly elastic sample S2, respectively. In a plastic sample, the material conforms closely to the shape of the tip T throughout the depth of the indent I, the contact area and indent area are essentially the same. In contrast, in a highly elastic sample, only a small portion of the tip above the apex A is embedded in the sample at the bottom of the indentation stroke. The remainder of the embedded portion of the tip T is surrounded by a free space extending radially from the tip T to the perimeter of the indent I, resulting in an indent area that is much larger than the area of the imbedded portion of the tip.
In addition, the lower limit of hcact, being the point of separation of the apex of the tip from the bottom of indentation during the unloading phase of the indentation cycle (hereafter referred to as the “release point”, Pr), is not the same as the deepest penetration point Pmax. This is because a sample having any significant elasticity will rebound as the tip is being withdrawn from the sample, resulting in a Pr that is above Pmax as seen in FIG. 13B. As a result, the actual contact depth hcact required for elastic modulus determination is reduced by the difference between Pmax and Pr.
A determination of hcact therefore requires a determination of the location of both the release point Pr where the apex of unloading tip first separates from the bottom of the rebounding indent, and the upper separation point, Psep, where no portion of the unloading tip contacts the detent.
The initial contact point, Pic, is often determined simply by determining the location at which the force imposed on the loading cantilever markedly changes during the loading phase of the indentation cycle. Referring to the force displacement curves 15 and 18 of FIG. 15, that point is relatively accurately determinable for a relatively hard surface which has a marked reaction to initial contact, evidenced by a “snap to contact” as a result of adhesive forces arising when the probe comes into close proximity with the sample surface, followed by a sharp increase in force as the probe is driven against the sample surface. That resistance is evidenced by the steep slope of the curve 15 after the initial “snap to contact” at point 16 in FIG. 15. However, in the case of a relatively soft sample such as a gel, the sample surface provides very little initial resistance to tip motion after the tip contacts the surface. The tip may drive well into the sample surface before the threshold resistance allegedly indicative of contact point is reached, resulting in an inaccurate determination of initial contact point. This problem can be appreciated by the very shallow and ill-defined slope of the curve 18 in FIG. 15.
A need therefore exists for a more accurate detection of initial contact point Pic, particularly in the case of indenting relatively soft samples.
Prior systems also have difficulty determining the release point, Pr, and the actual contact depth, hcact during indentation because material measurements are taken in a separate scanning operation sometime after the tip is removed from the indented sample. If the sample is relatively elastic or viscoelastic, creep, defined as changes in elastic deformation over time, will alter both the depth and area of the indent as the sample rebounds toward its original shape following initial tip removal.
In summary a quantitative mechanical property determination with cantilever probe based AFM the following aspects should be adequately addressed:
1. The load must be well defined. Since the cantilever sensor is primarily a flexural sensor, the lateral force along the cantilever axis is unknown and should be counteracted prior to determining load.
2. Contact points, including initial contact point, Pic, the release point, Pr, and the separation point, Psep, should be accurately measured.
3. With the knowledge of the tip shape, the contact area can be determined quantitatively.
Furthermore, the need has broadly arisen to provide a probe based instrument that is capable of obtaining high speed, high bandwidth quantitative measurement of mechanical properties through indentation and other interactions. It is believed that in order to meet these needs, the lateral component of AFM based indentation needs to be reduced by 2 to 3 orders of magnitude than is usually achievable using current techniques.
Partially in order to meet the above-identified need, and partially in order to achieve other benefits like more controlled tip-sample interaction, the need has also arisen to effectively and reliably counteract the lateral forces imposed on a probe as a result of probe-sample interaction.